# Lesson 1

Moving in Circles

### Problem 1

Here is a clock face. For each time given, name the number the second hand points at.

1. 15 seconds after 1:00.
2. 30 seconds after 1:00.
3. 1 minute after 1:00.
4. 5 minutes after 1:00.

### Solution

For access, consult one of our IM Certified Partners.

### Problem 2

At 12:15, the end of the minute hand of a clock is 8 feet above the ground. At 12:30, it is 6.5 feet off the ground.

1. How long is the minute hand of the clock? Explain how you know.
2. How high is the clock above the ground?

### Solution

For access, consult one of our IM Certified Partners.

### Problem 3

Here is a point on a circle centered at $$(0,0)$$.

Which equation defines the circle?

A:

$$x + y = 10$$

B:

$$x^2 + y^2 = 10$$

C:

$$x^2 + y^2 = 100$$

D:

$$(x-6)^2 + (y-8)^2 = 100$$

### Solution

For access, consult one of our IM Certified Partners.

### Problem 4

The point $$(3,4)$$ is on a circle centered at $$(0,0)$$. Which of these points lie on the circle? Select all that apply.

A:

$$(\text-3,\text-4)$$

B:

$$(4,3)$$

C:

$$(0,5)$$

D:

$$(0,0)$$

E:

$$(\text-5,0)$$

### Solution

For access, consult one of our IM Certified Partners.

### Problem 5

Match each polynomial with its end behavior as $$x$$ gets larger and larger in the positive and negative directions. (Note: some of the answer choices are not used and some answer choices may be used more than once.)

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 2, Lesson 19.)

### Problem 6

Find the solution(s) to each equation.

1. $$x^2-6x+8=0$$
2. $$x^2-6x+9=0$$
3. $$x^2-6x+10=0$$

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 3, Lesson 18.)